Last Updated: September 21, 2010

Betting Major League Baseball

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Introduction

The page will endeavor to give the recreational baseball bettor advice on the various bets. I have no handicapping skill in baseball whatsoever, so the best I can do is steer you towards the best type of bets. There are three primary ways to bet on baseball, as follows.

  • Money line: Bet on which team will win.
  • Total: Bet on whether the total number of runs will fall above or below a stated number, usually between 7 and 12.
  • Run line: Similar to a bet against the spread in football or basketball. However, in baseball the better team is always favored by 1.5. If the money line indicates neither team is favored, then either team could be the favored team.

Source of Data

The data this analysis is based on is from the Major League Baseball games played over the 10 years encompassing the 2000 to 2009 seasons. From the source data, I had to remove some games for lack of information, and I corrected many typographical errors. Basically, I felt the data was a bit rough, so please take my analysis below with a grain of salt.

Fun Facts

The following table shows the average number of runs, hits, errors, and bases from 2000 to 2009.

MLB Averages 2000-2009

Item Away Home Total1
Runs 4.68 4.83 9.52
Hits 9.17 9.05 18.22
Errors 0.65 0.63 1.29
Bases 15.65 15.59 31.23

Notes

1. Totals may not appear to agree with sum of the parts, due to rounding.

Following are some records from the "zeros" decade.

Money Line Bets

The following table shows the expected return on money line bets, according to every combination of home or away and favorite, pick or underdog. The table is crossed by whether the sports book uses a 10-cent, 15-cent or 20-cent line. For those unfamiliar with the term, a 10-cent line, for example, means the lines on the two teams are usually 10 points apart — for example +140 and -150.

It is not a typo that the table shows a player advantage for home underdogs of 2.07% against a 10-cent line. This may be partially due to a sampling error.

Money Line Bets in MLB

Bet on Sample Size 10-cent Line 15-cent Line 20-cent Line
Home favorite 15797 -1.81% -2.92% -3.99%
Home dog 7977 2.07% 0.92% -0.19%
Home pick 492 0.00% -1.13% -2.22%
Away favorite 7977 -4.94% -6.02% -7.05%
Away dog 15797 -1.88% -2.99% -4.05%
Away pick 492 -4.76% -5.84% -6.87%
All home 24266 -0.84% -1.97% -3.04%
All away 24266 -3.17% -4.27% -5.32%
All favorite 23774 -2.79% -3.89% -4.94%
All dog 23774 -0.55% -1.68% -2.76%
All pick 984 -2.38% -3.49% -4.55%
All 48532 -1.90% -3.01% -4.07%

Total Bets

The following table shows the winning side of total bets in each game.

Total Line Bets in MLB

Winner Sample Size Probability
Over 11315 46.63%
Under 11812 48.68%
Push 1139 4.69%
Total 24266 100.00%

Assuming the player lays 110 every time, the house edge is 6.29% on over bets and 2.38% on under bets. Seldom do casinos have total bets with less juice than 10 cents.

Run Line Bets

Unfortunately, my data does not indicate the run line bets. However, I can offer the following tables to help determine the fair run line according to the fair money line (F.M.L.) and total. I used logistic regression to create these tables, which was no easy task.

The first table is for away underdogs +1.5 runs. To get the fair money line the other way, on a home favorite -1.5 runs, take the opposite line by multiplying by -1.

Fair Run Lines for Away Underdogs +1.5

F.M.L. Total
7 7.5 8 8.5 9 9.5 10 10.5 11 11.5 12
100 -212 -207 -203 -199 -195 -191 -187 -183 -180 -176 -173
105 -203 -199 -195 -191 -187 -183 -179 -176 -172 -169 -165
110 -195 -191 -187 -183 -180 -176 -172 -169 -165 -162 -159
115 -188 -184 -180 -176 -173 -169 -166 -163 -159 -156 -153
120 -181 -177 -174 -170 -167 -163 -160 -157 -154 -150 -147
125 -175 -171 -168 -164 -161 -158 -154 -151 -148 -145 -142
130 -169 -165 -162 -159 -156 -152 -149 -146 -143 -140 -138
135 -164 -160 -157 -154 -151 -148 -145 -142 -139 -136 -133
140 -159 -155 -152 -149 -146 -143 -140 -137 -135 -132 -129
145 -154 -151 -148 -145 -142 -139 -136 -133 -131 -128 -125
150 -150 -147 -144 -141 -138 -135 -132 -130 -127 -124 -122
155 -146 -143 -140 -137 -134 -131 -129 -126 -124 -121 -119
160 -142 -139 -136 -133 -131 -128 -125 -123 -120 -118 -116
165 -138 -136 -133 -130 -127 -125 -122 -120 -117 -115 -113
170 -135 -132 -130 -127 -124 -122 -119 -117 -115 -112 -110
175 -132 -129 -127 -124 -122 -119 -117 -114 -112 -110 -108
180 -129 -126 -124 -121 -119 -116 -114 -112 -109 -107 -105
185 -126 -124 -121 -119 -116 -114 -112 -109 -107 -105 -103
190 -124 -121 -119 -116 -114 -112 -109 -107 -105 -103 -101
195 -121 -119 -116 -114 -112 -109 -107 -105 -103 -101 101
200 -119 -116 -114 -112 -109 -107 -105 -103 -101 101 103
210 -114 -112 -110 -108 -105 -103 -101 101 103 105 107
220 -110 -108 -106 -104 -102 100 102 104 107 109 111
230 -107 -105 -103 -101 102 104 106 108 110 112 115
240 -104 -102 101 103 105 107 109 111 114 116 118
250 -101 101 103 106 108 110 112 115 117 119 122
260 102 104 106 109 111 113 115 118 120 123 125
270 105 107 109 111 114 116 118 121 123 126 129
280 107 110 112 114 117 119 121 124 127 129 132
290 110 112 115 117 119 122 124 127 130 132 135
300 112 115 117 120 122 125 127 130 132 135 138
310 115 117 120 122 125 127 130 133 135 138 141
320 117 120 122 125 127 130 132 135 138 141 144
330 119 122 124 127 130 132 135 138 141 144 147
340 122 124 127 129 132 135 138 140 143 146 149
350 124 126 129 132 134 137 140 143 146 149 152
360 126 128 131 134 137 139 142 145 148 151 154
370 128 131 133 136 139 142 145 148 151 154 157
380 130 133 135 138 141 144 147 150 153 156 159
390 132 135 137 140 143 146 149 152 155 159 162
400 134 136 139 142 145 148 151 154 158 161 164

Let's take a look at an example to see how to use the table. On April 6, 2010, the Las Vegas Hilton offered the following bets on the Yankees vs. Red Sox game. As always, the home team is listed last.

Yankees vs. Red Sox

Team Money Line Total Run Line
Yankees 125 9.5 -170
Red Sox -135 150

The fair line on the Yankees would be +130, which can be found by splitting the juice between the two teams. Next, look up the value in the table for +130 and 9.5, which is -152. So fair run line bets would be:

Yankees +1.5 -152
Red Sox -1.5 +152

The actual run lines are -170 and +150. Assuming my analysis was correct, the house edge on the Yankees run line would be 4.20% and on the Red Sox it would be 0.79%.

By the way, the actual score of the game was Yankees 6, Red Sox 4.

The next table shows the fair run lines for home underdogs. The reason for the significant difference between it and the away underdog table above is because it is more valuable to get the extra 1.5 runs on an away team. This is because the game will be over after any winning play by the home team in the 9th or later inning. Thus, there are a lot of games where the home team wins by one run.

Fair Run Lines for Home Underdogs +1.5

F.M.L. Total
7 7.5 8 8.5 9 9.5 10 10.5 11 11.5 12
100 -171 -169 -168 -166 -165 -163 -162 -160 -159 -157 -156
105 -164 -162 -161 -159 -158 -156 -155 -153 -152 -150 -149
110 -157 -156 -154 -153 -151 -150 -148 -147 -146 -144 -143
115 -151 -150 -148 -147 -145 -144 -143 -141 -140 -139 -137
120 -145 -144 -143 -141 -140 -139 -137 -136 -135 -134 -132
125 -140 -139 -138 -136 -135 -134 -133 -131 -130 -129 -128
130 -136 -134 -133 -132 -130 -129 -128 -127 -126 -124 -123
135 -131 -130 -129 -127 -126 -125 -124 -123 -122 -120 -119
140 -127 -126 -125 -123 -122 -121 -120 -119 -118 -117 -116
145 -123 -122 -121 -120 -119 -118 -116 -115 -114 -113 -112
150 -120 -119 -117 -116 -115 -114 -113 -112 -111 -110 -109
155 -116 -115 -114 -113 -112 -111 -110 -109 -108 -107 -106
160 -113 -112 -111 -110 -109 -108 -107 -106 -105 -104 -103
165 -110 -109 -108 -107 -106 -105 -104 -103 -102 -101 -100
170 -108 -107 -106 -105 -104 -103 -102 -101 100 101 102
175 -105 -104 -103 -102 -101 -100 101 102 103 104 105
180 -103 -102 -101 100 101 102 103 104 105 106 107
185 -100 100 101 102 103 104 105 106 107 108 109
190 102 103 104 105 106 107 108 109 110 111 112
195 104 105 106 107 108 109 110 111 112 113 114
200 106 107 108 109 110 111 112 113 114 115 117
210 110 111 112 113 114 115 117 118 119 120 121
220 114 115 116 117 119 120 121 122 123 124 126
230 118 119 120 121 123 124 125 126 127 129 130
240 122 123 124 125 127 128 129 130 132 133 134
250 126 127 128 129 130 132 133 134 136 137 138
260 129 130 132 133 134 136 137 138 139 141 142
270 133 134 135 137 138 139 141 142 143 145 146
280 136 137 139 140 141 143 144 145 147 148 150
290 139 141 142 143 145 146 148 149 150 152 153
300 143 144 145 147 148 150 151 152 154 155 157
310 146 147 149 150 151 153 154 156 157 159 160
320 149 150 152 153 155 156 158 159 161 162 164
330 152 153 155 156 158 159 161 162 164 165 167
340 155 156 158 159 161 162 164 165 167 169 170
350 158 159 161 162 164 165 167 168 170 172 173
360 160 162 163 165 167 168 170 171 173 175 176
370 163 165 166 168 169 171 173 174 176 178 179
380 166 167 169 170 172 174 175 177 179 180 182
390 168 170 171 173 175 176 178 180 181 183 185
400 171 172 174 175 177 179 181 182 184 186 188

Alternate Totals

It often happens when you want to make an over or under bet in baseball that there are two different totals available. For example, 7.5 and 8. Of course, you have to pay a higher price if you want the half point to work in your favor. The price will depend on whether you are buying or selling an odd or an even number, because in baseball, odd totals are more common than even ones. During the zeros decade (somebody please come up with a term for it), 59.2% of Major League Baseball games ended in an odd total. Hopefully I don't need to explain why. The following tables shows the fair equivalent price to pay for buying an extra half point off either an over or under bet.

To use the table, look up the line on the lower of the two lines if betting the under, and the higher if betting the over. Whether you use the second or third column will depend on whether you're looking at an over or under bet, and whether the base line is odd, even, odd +0.5, or even +0.5. To be specific, if you're interested in the under, use the second column for an odd or even +0.5 base number, otherwise use the third column. If you're interested in the over, use the second column for an odd or odd +0.5 base number, otherwise use the third column.

Alternative Totals for Buying a Half Point

Market Line Off the Under
Odd, Even +0.5 Even, Odd +0.5
Off the Over
Odd or Odd +0.5 Even or Even +0.5
-140 -177 -165
-135 -170 -159
-130 -164 -153
-125 -157 -147
-120 -151 -141
-115 -144 -135
-110 -138 -129
-105 -131 -123
100 -125 -117
105 -119 -111
110 -114 -106
115 -109 -102
120 -104 103
125 -100 107
130 104 111
135 108 115
140 112 119

Let's look at an example of how to use the table. In the Astros vs. Marlins game today (Aug. 20, 2010) as I write this, you can get under 7.5 at the Hilton for -105 or under 8 at the MGM for -135. Which is the better bet? 7.5 is an "odd +0.5" number. The -105 row and the "even, odd +0.5" column meet at -123. That means you should be indifferent between betting under 7.5 -105 and under 8 -123. The actual MGM price was -135, so in this example the under 7.5 -105 at the Hilton is the better bet.

The next table shows the fair price to pay if you want to buy a half point off of an over bet. For example, in the same Astros vs. Marlins game, you can bet over 7.5 at -115 at the Hilton or over 8 at +115 at the MGM. Which is the better bet? We should use 8 as the base line, because the alterative of 7.5 is a half-point better. So looking at the +115 row and the "even or even +0.5" column we see the fair equivalent is -102. The Hilton price on over 7.5 is -115, which is worse than -102, making over 8 +115 at the MGM the better bet.

Let's look at some more examples. Here are some lines from the Braves Vs. Cubs game.

Hilton: Over 10 -115, Under 10 -105
MGM: Over 10.5 EV, Under 10.5 -120

If we assume under 10 -105 to be fair, then the equivalent bet is under 10.5 -123. So the under 10.5 -120 at the MGM is better. If we assume over 10.5 EV to be fair, then the equivalent bet is over 10 -117. So the over 10 -115 at the Hilton is better.

Next, here are lines from the Bluejays vs Red Sox game.

Stations: Over 8.5 -105, Under 8.5 -115
Hilton: Over 8 -125, Under 8 +105

If we assume under 8 +105 to be fair, then the equivalent bet is under 8.5 -111. The under 8.5 -115 at Stations is not as good, so under 8 +105 is the better bet. If we assume over 8.5 -105 to be fair, then the equivalent bet is over 8 -123. The over 8 -125 at the Hilton is not as good, so the over 8 -105 is the better bet.

Total Runs, Hits, and Errors

Sometimes in the post-season, the casinos will offer an over/under prop on the total combined runs, hits and errors. I noticed there is a fairly linear relationship between the projected total and the actual total of runs, hits and errors. The least-squares regression line for the estimated total runs, hits and errors is 12.45 + 1.817 × t, where t represented the estimated total.

The following table shows the estimated and actual total runs, hits and errors according to the projected total runs.

Total Combined Runs, Hits and Errors in MLB

Total Sample Size Estimated Actual
6 1 23.35 14.00
6.5 71 24.26 24.46
7 610 25.17 24.81
7.5 1635 26.08 26.36
8 2393 26.98 26.74
8.5 4122 27.89 27.80
9 5337 28.80 28.88
9.5 4472 29.71 29.92
10 2395 30.62 30.53
10.5 1736 31.53 31.42
11 747 32.43 32.22
11.5 285 33.34 33.75
12 131 34.25 33.80
12.5 102 35.16 33.61
13 77 36.07 35.97
13.5 55 36.98 36.73
14 47 37.89 35.96
14.5 35 38.79 40.29
15 15 39.70 45.33

Run Scored in First Inning

A popular proposition bet in baseball is whether or not a run will be scored in the first inning. It is pretty obvious that the probability of a run in the first inning would be highly correlated to the projected total. The following table shows the number of games with a run in the first inning, according to the total. The second column, titled RSFI, stands for "Run Scored in the First Inning." This table was based on the 2001 to 2011 seasons. The lower right cell shows an overall probability of at least one run in the first inning of 52.5%.

Run Scored in First Inning Data

Total RSFI Total Games Ratio
5 0 1 0.00%
5.5 13 17 76.47%
6 30 68 44.12%
6.5 134 335 40.00%
7 537 1127 47.65%
7.5 1093 2313 47.25%
8 1544 3109 49.66%
8.5 2603 5039 51.66%
9 3054 5859 52.12%
9.5 2415 4403 54.85%
10 1199 2163 55.43%
10.5 811 1358 59.72%
11 313 516 60.66%
11.5 128 206 62.14%
12 72 112 64.29%
12.5 64 103 62.14%
13 47 68 69.12%
13.5 26 41 63.41%
14 10 16 62.50%
14.5 8 12 66.67%
15 1 1 100.00%
Total 14102 26867 52.49%

Here is what that looks like in a graph. The blue line shows the actual percentage of games with a run in the first inning by estimated total runs, from 6.5 to 11.5. The red line is called a "least-squared" regression line, which smooths out the ups and downs by showing the line that best matches the game total to the probability of a first-inning run. The equation for that line is p=0.2554 + 0.0304×t, where p = probability of first-inning run, and t=estimated total runs.

I also considered whether it mattered if the game had a big favorite. Given the same total, I found that that money lines on the game didn't affect the probability of a first-inning run.

In baseball, the odds are often different depending on whether a bet is on the under or over the projected total runs. For example, in a game on April 13, 2012, between the Brewers and Braves the total is 7.5. At Bovada, the line on the over is -125, and on the under is +105. Given the pressure on a high total, that would indicate an increased probability of a run in the first inning. What I suggest to adjust for that is to use the following modified formula when there is unequal demand between the over and under.

p = 0.2554 + 0.0304×t + 0.000724×f, where

p = Probability of first-inning run
t = Projected game total
f = Favoritism points on the over

Let me explain "favoritism points on the over." This is how many point the money line on the over has moved in the direction of the over being the favorite side. For example, if the sports book has a 20-cent line on the total, meaning the under and over are 20 points apart, then the following table shows the number "favoritism points on the over."

Favoritism Points on the Over

Money Line
on Over
Favoritism
Points
130 -40
125 -35
120 -30
115 -25
110 -20
105 -15
100 -10
-105 -5
-110 0
-115 5
-120 10
-125 15
-130 20
-135 25
-140 30
-145 35
-150 40

Let's look at a couple of examples, based on a 20-cent total.

Example 1: Mets vs. Phillies, over 6.5 -115. The table above shows 5 favoritism points. So the probability of a run in the first inning is:

p = 0.2554 + 0.0304×6.5 + 0.000724×5 = 0.45662. That equates to a fair line on a first-inning run of +119.

Example 2: Orioles vs. Yankees, over 7.5 -105. The table above shows -5 favoritism points. So the probability of a run in the first inning is:

p = 0.2554 + 0.0304×7.5 + 0.000724×-5 = 0.47978. That equates to a fair line on a first-inning run of +108.

If you're using a sports book with other than a 20-cent line on the total, then adjust the favoritism points accordingly.

A look at actual lines on this prop shows that most sports books set them well enough to not find an advantage either way. However, I found one book that seemed to favor the "no" on this prop, often making betting on a first-inning run a good value. It is good to try to bet at such places early, to beat the other sharp bettors.

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